Limits and Continuity

Given the function $f(x)$ whose graph includes an inflection point at $(3, 7)$, if $g(x) = f'(x - 2) + 5$, at which $x$-value would the graph of $g$ exhibit a potential local extremum?

When estimating a limit value from a graph, if the y-values from the left and right sides approach different values, but the difference between these values gets smaller and smaller, what can be concluded about the limit?

What is $\lim_{x \to +\infty} f(x)$ if the graph has a horizontal asymptote at y=7?

When estimating a limit value from a graph, if the y-values from the left and right sides approach different infinities (positive and negative), what can be concluded about the limit?

If $\lim_{h \to 0} \frac{f(a+h)-f(a)}{h} = L$, what is $\lim_{h \to 0} \frac{4[f(a+2h)-f(a)]}{h}$ assuming that f is differentiable at 'a'?

Based on a graph showing that as x nears negative infinity for function j, j's outputs seem to stabilize around negative seven, how do you denote this observed behavior using limits?

For a function $f$, as $x$ approaches a certain value from both sides, the $y$-values diverge and do not approach the same value. What can be concluded about the limit of $f$ as $x$ approaches that value?

When estimating a limit value from a graph, if the y-values from the left and right sides approach different values and the difference between these values increases without bound, what can be concluded about the limit?

If the y-values from the left side and the right side of a specific x-value are different on a graph, what can be concluded about the limit at that x-value?

For continuous function $k(t)$, if the first derivative $k'(t)$ has one real root $r$ and second derivative $k''(t)$ has three real roots with one being $r$ as well, what can be deduced about $k(t)$'s graph near $t=r$?